Thursday, June 6, 2013

Scott Aaronson recently uploaded a mind-boggling paper, full of challenging ideas regarding free-will, quantum mechanics and computing, philosophical big questions, neuroscience, and many other hot topics. The title is The Ghost in the Quantum Turing Machine, and will be a chapter in the book The Once and Future Turing, edited by S. Barry Cooper and Andrew Hodges, 2013.

His paper is like a storm of puzzle pieces, which fit together perfectly in an amazing tapestry, centered around his idea of Knightian freedom.

Here is the abstract

In honor of Alan Turing's hundredth birthday, I unwisely set out some
thoughts about one of Turing's obsessions throughout his life, the question of
physics and free will. I focus relatively narrowly on a notion that I call
"Knightian freedom": a certain kind of in-principle physical unpredictability
that goes beyond probabilistic unpredictability. Other, more metaphysical
aspects of free will I regard as possibly outside the scope of science. I
examine a viewpoint, suggested independently by Carl Hoefer, Cristi Stoica, and
even Turing himself, that tries to find scope for "freedom" in the universe's
boundary conditions rather than in the dynamical laws. Taking this viewpoint
seriously leads to many interesting conceptual problems. I investigate how far
one can go toward solving those problems, and along the way, encounter (among
other things) the No-Cloning Theorem, the measurement problem, decoherence,
chaos, the arrow of time, the holographic principle, Newcomb's paradox,
Boltzmann brains, algorithmic information theory, and the Common Prior
Assumption. I also compare the viewpoint explored here to the more radical
speculations of Roger Penrose. The result of all this is an unusual perspective
on time, quantum mechanics, and causation, of which I myself remain skeptical,
but which has several appealing features. Among other things, it suggests
interesting empirical questions in neuroscience, physics, and cosmology; and
takes a millennia-old philosophical debate into some underexplored territory.

Recently, a new paper by Maldacena and Susskind appears, named Cool horizons for entangled black holes (arxiv:1306.0533). In the paper, the two authors propose that two entangled particles are connected by an Einsten-Rosen bridge, a wormhole. Their stake is in fact related to the black hole information paradox, the Maldacena correspondence, and the recent idea of black hole firewalls. It was covered, among others, by Sean Carroll.

AN EXPLICIT LOCAL VARIABLES TOPOLOGICAL MECHANISM FOR THE EPR CORRELATIONS

It is based on a non-trivial topology (wormholes).

Cut
two spheres out of our space, and glue the two boundaries of the space
together. This wormhole can be traversed by a source free electric
field, and used to model a pair of electrically charged particles of
opposite charges as its mouths (Einstein-Risen 1935, Misner-Wheeler's
charge-without-charge 1957, Rainich 1925).

For EPR we need a
wormhole which connects two electrons instead of an electron-positron
pair. A wormhole having as mouths two equal charges can be obtained as
follows: instead of just gluing together the two spherical boundaries,
we first flip the orientation of one of them. Since the electric field
is a bivector, the change in orientation changes the sign of the
electric field, and the two topological charges have the same sign.

Now
associate to the two electrons your favorite local classical
description. The communication required to obtain the correlation can be
done through the wormhole.

----------------

This may be
the basis of a mathematically correct local hidden variable theory.
Also, it seems to disprove, or rather circumvent, Bell's theorem. For
Bohm's hidden variable theory, it provides a mechanism to get the
correlation without faster than light signals. I proposed it here for
theoretical purposes only, as an example. My favorite interpretation is another one.

Cristi

I did not want to spend more time on this, only to break my neck proposing local models of entanglement, especially since I did not find the idea of hidden variables relevant.